Bifurcation and chaos analysis for multi-freedom gear-bearing system with time-varying stiffness

This study performs a systematic dynamic analysis of a gear-bearing system with time varying stiffness, gear backlash and surface friction. At first the period expansion method is proposed to build a six-degree-of freedom nonlinear dynamic model of a spur gear pair. Then the dynamic orbits of the system are observed using the bifurcation diagrams with the mesh stiffness and the rotational speed ratio as control parameters. And the onset of chaotic motion is identified from the phase diagrams, FFT spectra, Poincaré maps and the largest Lyapunov exponents of the gear-bearing system. The numerical results reveal that the system enters into chaotic motion under several frequency jumps with the increase of excitation frequency. When the support stiffness is raised, the number of frequency jumps increases, and the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors. In this study the results provide a useful source of reference for engineers and technicians in designing and controlling such systems.